Optimal 3-dimensional search model to find the underwater randomly hidden target (Q2247686)

Summary: The searcher's path for finding a 3-dimensional underwater randomly located target like a black box for the air plan crash is studied. The searcher moves along slinky-turn-spiral curve and starts its motion from a known point \((X_0, Y_0, Z_0)\). We focus on the geometry features such as curvature and torsion of the search path for the target position that has a known distribution. The searcher is desired to search in an optimal manner by obtaining the optimal values of the curvature and the torsion that minimise the expected time for detecting the target. An illustrative example has been given to demonstrate the applicability of this technique.